Incompleteness of the Landauer Formula for Electronic Transport

Details Incompleteness of the Landauer Formula for Electronic Transport Incompleteness of the Landauer Formula for Electronic Transport

2008-10-16

arxiv.org/abs/0810.2857v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

11 pages, 4 figures, submitted to Phys. Rev. B

Scientific paper

10.1103/PhysRevB.79.014201

We show that the Landauer multi-terminal formula for the conductance of a nanoscale system is incomplete because it does not take into account many-body effects which cannot be treated as contributions to the single-particle transmission probabilities. We show that the physical origin of these effects is related to the viscous nature of the electron liquid, and develop a perturbative formalism, based on the time-dependent current-density-functional theory, for calculating the corrections to the resistance in terms of the ``Kohn-Sham current distribution'' and the exchange-correlation kernel. The difficulties that still remain in calculating the latter are critically discussed.

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